Although they might not express themselves in quite this way, non-philosophers tend to think that mereological composition is a vague matter : sometimes it occurs, sometimes it does not, and sometimes it sort of occurs. For example, when I am building a boat, at ﬁrst the timbers that I have acquired for the job do not jointly compose an entity; in the end they do—they compose the boat that I have built; and in between they sort of or more or less or to some extent compose an entity, which in turn sort of or more or less or to some extent exists—this entity being the boat I am building. This idea seems innocuous enough. However, the orthodox view amongst philosophers is that composition can never be a vague matter, because vague composition entails vague existence (the common-sense view agrees with this step), and vague existence is impossible if not nonsensical. Let us call the following the ‘orthodox argument’.